Lots of kids give up naps of all kinds somewhere between 1 and 2. Having a routine quiet-time a couple of times a day remains an excellent plan. Sitting quietly doing quiet things will all of the electronic noisemakers and lights off in the house will give everyone a rest, even if you only get to put your feet up and inhale a cup of tea.
Make it a happy family routine, be absolutely convinced that everyone needs it, and at least for now lie down with both of them so neither have the idea that there is something 'going on' that they're missing out on. Peer pressure works on little kids... if you stay still and quiet, and breath in a long, deep and slow pattern, they'll match it if they're close to you, and probably fall asleep even though they 'don't need a nap'... until they're 5 or 6, if you really do take the opportunity to rest alongside them...